Answered: A sales manager collected the following…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 30PT: For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or...

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Question

A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is

ŷ = 81 + 4x.

Salesperson	Years of Experience	Annual Sales ($1,000s)
1	1	80
2	3	97
3	4	92
4	4	107
5	6	103
6	8	111
7	10	119
8	10	128
9	11	117
10	13	136

(a)

Compute the residuals.

Years of Experience	Annual Sales ($1,000s)	Residuals
1	80
3	97
4	92
4	107
6	103
8	111
10	119
10	128
11	117
13	136

Construct a residual plot.

A residual plot has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from −16 to 16 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. There are 6 points below the line and 4 points above the line. The points are between 1 to 13 on the horizontal axis and appear to vary randomly between −8 to 10 on the vertical axis. The maximum residual is at 4 years of experience while the minimum is at 11 years of experience.

A residual plot has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from −16 to 16 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. There are 4 points below the line and 6 points above the line. The points are between 1 to 13 on the horizontal axis and appear to vary randomly between −10 to 8 on the vertical axis. The maximum residual is at 11 years of experience while the minimum is at 4 years of experience.

A residual plot has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from −16 to 16 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. There are 6 points below the line and 4 points above the line. The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the plot. The points are between 1 to 13 on the horizontal axis and between −8 to 10 on the vertical axis.

A residual plot has 10 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Years of Experience. The vertical axis ranges from −16 to 16 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. There are 6 points below the line and 4 points above the line. The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the plot. The points are between 1 to 13 on the horizontal axis and between −8 to 10 on the vertical axis.

(b)

Do the assumptions about the error terms seem reasonable in light of the residual plot?

The plot suggests a generally horizontal band of residual points indicating that the error term assumptions do not appear reasonable.The plot suggests a funnel pattern in the residuals indicating that the error term assumptions do not appear reasonable. The plot suggests curvature in the residuals indicating that the error term assumptions appear reasonable.The plot suggests a generally horizontal band of residual points indicating that the error term assumptions appear reasonable.The plot suggests a funnel pattern in the residuals indicating that the error term assumptions appear reasonable.

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